Asquare is inscribed in a right triangle so that they have a common right angle. the legs of the triangle are 6 in and 8 in long. find the length of the side of the square.

  24/7 = 3 3/7 inches

Step-by-step explanation:

The triangle can be represented by a line in the first quadrant with y-intercept 8 and x-intercept 6. Then its equation is ...

  x/6 +y/8 = 1 . . . . . intercept form of the equation of the line

  4x + 3y = 24 . . . . multiply by 24 to get standard form

Since the square will have the origin as one corner, and all sides are the same length, the opposite corner will lie on the line y=x. Then we're solving the system ...

  4x +3y = 24

  y = x

to find the side length.

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By substitution for y, this becomes ...

  4x +3x = 24

  7x = 24

  x = 24/7 = 3 3/7

The length of the side of the square is 3 3/7 inches.

m∠a is 90°

m∠b is 40°

explanation:

step-by-step explanation: